# Simulation model Homework Assignment 2015

August 30, 2017

Question

Submit the R codes that show your simulation model along with your homework submission. Include a separate R code file.

Clearly indicate the steps in all your simulation models – what random variables form the input and what are their distributions, what is the output that you are measuring and the functional relation between the output and the input random variables.

In all your simulations, set the number of trials to 1000. Use Monte Carlo sampling, sampling type as Monte Carlo and the generator as Mersenne Twister.

Question

The revenues and costs at ABC Company vary from month to month and can be modeled

as random variables. ABC estimates (based on past data) that its sales, cost of goods sold

(COGS), marketing costs, administrative costs and miscellaneous costs for the month of

Januaryhave the following distributions:

January figures

Sales

Normal(2225,150)

COGS

Uniform(870, 910)

Marketing cost

Triangular (90, 93, 96)

Triangular (75, 78, 81)

Miscellaneous cost

Triangular (23, 24, 25)

In addition, the percentage change in the sales, COGS, marketing, administrative and

miscellaneous costs from one month to the next can be modeled as independentnormal

random variables with a mean of 1.5% and a standard deviation of 1%. For example,

SalesFeb = SalesJan(1 + XJan-Sales), COGSFeb = COGSJan(1+XJan-COGS) etc., where XJan-Sales

denotes the percentage change in sales from Jan to Feb, XJan-COGS denotes the percentage change in COGS from Jan to Feb. XJan-Sales and XJan-COGS are independent Normal(1.5%,

1%) random variables. In addition, the tax rate is 33%.

Estimate the annual net income of ABC after taxes.

Give the mean and the standard deviation.

Note that Net Income after taxes (in a month) = Net Income before taxes –Tax, where

· Net income before taxes = Gross Margin – Total expenses

· Gross margin = Sales – Cost of goods sold

· Total expenses = Marketing costs + Administrative costs + Miscellaneous costs

· Tax = Tax rate*Net Income before taxes

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